


MEASUREMENT OF FREQUENCY OF A VOLTAGE SIGNALThe patterns obtained on CRO screen and discussed in previous sections are called the Lissajous patterns. ALissajous pattern is a pattern which is stationary on the screen of a CRO. It means that the spot traces out the same pattern for every cycle of a voltage signal. As we have already studied that the ratio of frequencies of vertical and horizontal voltage signals should be a rational or fractional number to have steady pattern. So the condition for having a Lissajous pattern on the CRO screen is F_{y}/ F_{x}= A/B, where A and B are integers. Lissajous patterns are usually of two types. First one is closed Lissajous pattern and has no free end. Second one is open Lissajous pattern and has free ends. Both types of Lissajous patterns are shown in figure. In a Lissajous pattern ratio of frequency of vertical signal to the frequency of horizontal signal is equal to the ratio of positive Ypeaks to positive Xpeaks in that pattern. F_{y}/ F_{x}=Positive Y – peaks in pattern /Positive X – peaks in pattern Thus by counting the positive Ypeaks and Xpeaks on a Lissajous pattern, ratio of frequencies of two voltage signals can be determined. In case of an open lissajous pattern, free end is treated as half peak. This will be clear from examples. Voltage signal of unknown frequency is applied to the vertical deflection plates and horizontal deflection plates are supplied by an accurately calibrated variable frequency source. Frequency of the variable frequency source is adjusted until a stationary pattern appears on the screen. Now by reading the value of frequency of horizontal signal, with the help of calibrated scale, frequency of voltage signal applied to vertical deflection plates can be known.
Lissajous Patterns
In case single loop stationary pattern is obtained the frequency of the sinusoidal voltage applied to vertical deflection pates is the same as that of the voltage applied to horizontal deflection plates. In case complex Lissajous figure is obtained, the frequency of alternating voltage may be determined using the relation Points of tangency to a vertical line / Points of tangency to a horizontal line = ω_{x}/ω_{y} = f_{x}/f_{y} One point, very interesting, to know is that sometimes we may have different types of patterns on the CRO screen for the voltage signals of the given frequencies, as shown in figure. In both of the figures, the ratio of Ypeaks to Xpeaks is equal so in both cases, ratios of frequencies of vertical and horizontal signals are same. But appearance of Lissajous patterns is different owing to different phase difference of voltage signals applied to vertical arid horizontal deflection plates. CRO is not a precision instrument for measuring frequency of an alternating voltage because the accuracy depends directly on the accuracy of calibrated scale of variable frequency source, which is usually a few percent. It is used for rough estimate of frequency or when voltage waveform is so complex that a frequency counter would not operate reliably. 
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